Singular and regular solutions of a non-linear parabolic system
Petr Plechac, Vladimir Sverak
Abstract
We study a dissipative nonlinear equation modelling certain features of the Navier-Stokes equations. We prove that the evolution of radially symmetric compactly supported initial data does not lead to singularities in dimensions n≤ 4. For dimensions n>4 we present strong numerical evidence supporting existence of blow-up solutions. Moreover, using the same techniques we numerically confirm a conjecture of Lepin regarding existence of self-similar singular solutions to a semi-linear heat equation.
Create a lesson
Related papers
Positive normalized solutions for a singular regularized p(x)-Laplacian Dirichlet problem
Mustafa Avci
Regularity for axisymmetric Navier-Stokes with an Euler length
Peter Constantin, Mihaela Ignatova, Vlad Vicol
Existence of strong initial traces for stochastic conservation laws
Marko Erceg, Nikola Konatar, Kenneth Karlsen et al.
Asymptotics of nonlocal nonlinear Robin energies
Serena Dipierro, Giuseppe Spadaro, Enrico Valdinoci
Discontinuity of the Vlasov--Poisson Flow in LxpLv∞
Ke Chen, In-Jee Jeong, Quoc-Hung Nguyen et al.
Dense orbits for scale-invariant rotationally symmetric solutions of the 2D Euler equations
Ibrahim Suleiman